Chapter 7
Section 7.1/5:
a)
Reflexive: We have that
, so it is reflexive
Symmetric: It is not true that from
. For example
Antisymmetric:From
antisymmetric.
but
does not divide .
. But
Transitive:Let
. So it is
transitive
b)
Reflexive: We have that
, so i
Describe a situation in your professional or personal life when recursion, or at least the principle
of recursion, played a role in accomplishing a task, such as a large chore that could be
decomposed into smaller chunks that were easier to handle separat
Describe a favorite recreational activity in terms of its iterative components, such as solving
a crossword or Sudoku puzzle or playing a game of chess or backgammon. Also, mention
any recursive elements that occur.
I sometimes enjoy doing crossword puzzl
How does Boolean algebra capture the essential properties of logic operations and set
operations?
Boolean algebra also known as abstract algebra/algebraic structure (which are a collection of
elements and operations on them obeying defining axioms) that c
Chapter 1Supplementary Exercises
Problem 1
In the manufacture of a certain type of automobile, four
kinds of major defects and seven kinds of minor defects can
occur. For those situations in which defects do occur, in how
many ways can there be twice as m
You are an electrical engineer designing a new integrated circuit involving potentially millions of
components. How would you use graph theory to organize how many layers your chip must
have to handle all of the interconnections, for example? Which proper
Week 1 DQ 1
Sometimes, political leaders make statements appealing to emotion and give the
impression that holding a middle-ground position is not an option. President George
W. Bush used this type of appeal after September 11th, 2001 by stating, Either y
Conjunctive and disjunctive normal forms provide a form of balanced expression. How might
this be important in terms of the efficiency of computational evaluation?
The problem of efficiently evaluating a large collection of complex Boolean expressions bey
How does the reduction of Boolean expressions to simpler forms resemble the traversal of a
tree, from the Week Four material? What sort of Boolean expression would you end up with at
the root of the tree?
Both Boolean Expressions and Traversal of a Tree h
Trees occur in various venues in computer science: decision trees in algorithms, search trees,
and so on. In linguistics, one encounters trees as well, typically as parse trees, which are
essentially sentence diagrams, such as those you might have had to
Random graphs are a fascinating subject of applied and theoretical research. These can be
generated with a fixed vertex set V and edges added to the edge set E based on some
probability model, such as a coin flip. Speculate on how many connected component
How is the principle of inclusion and exclusion related to the rules for manipulation and
simplification of logic predicates you learned in Ch. 2?
The inclusionexclusion principle (also known as the sieve principle) is an equation relating the
sizes of tw
Look up the term axiom of choice using the Internet. How does the axiom of choicewhichever
form you preferoverlay the definitions of equivalence relations and partitions you learned in
Ch. 7?
In mathematics, the axiom of choice, or AC, is an axiom of set
What sort of relation is friendship, using the human or sociological meaning of the word? Is it
necessarily reflexive, symmetric, antisymmetric, or transitive? Explain why or why not. Can the
friendship relation among a finite group of people induce a par
There is an old joke, commonly attributed to Groucho Marx, which goes something like this: I
dont want to belong to any club that will accept people like me as a member. Does this
statement fall under the purview of Russells paradox, or is there an easy s
There is an old joke that goes something like this: If God is love, love is blind, and Ray Charles
is blind, then Ray Charles is God. Explain, in the terms of first-order logic and predicate
calculus, why this reasoning is incorrect.
First, let's break do
Consider the problem of how to arrange a group of n people so each person can shake hands
with every other person. How might you organize this process? How many times will each
person shake hands with someone else? How many handshakes will occur? How must
Mathematical Concepts of Computer Vision
Team A
MTH-221
February 23, 2013
Bruce Stephan
Introduction
Algorithmic Concepts
Edge Detection
Image Variations
Artificial Intelligence
Edge Detection
Edges
are high value information in
an image
Edges
generally m
Chapter 15 Supplemental Problems
Problem 1:
a) Note that
. So the left hand side is
if and only if all the
variables are , otherwise it is . Now the right hand side: if some of the variables are
then the expression is . So the right hand side is
if and on
Chapter 11
Section 11.1/3
Problem 2:
(a) Such a walk is
(b) Such a trail is
but it is not a trail because not all edges are distinct (
but it is not a path because the vertex
)
is repeated
(c)
(d) Such walk is
repeated
but it is not a closed circuit becau
Sec 4.1 /4
4.Awheel of fortune has the integers from 1 to 25 placed on it
in a random manner. Show that regardless of how the numbers
are positioned on the wheel, there are three adjacent numbers
whose sum is at least 39.
Answer
Since all the numbers are
Using a search engine of your choice, look up the term one-way function. This concept arises in
cryptography. Explain this concept in your own words, using the terms learned in Ch. 5
regarding functions and their inverses.
One-way functions are functions